MinT - Best Known (174−47, 174, s)-Nets in Base 3

Best Known (174−47, 174, s)-Nets in Base 3

(174−47, 174, 288)-Net over F₃ — Constructive and digital

Digital (127, 174, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 58, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(174−47, 174, 565)-Net over F₃ — Digital

Digital (127, 174, 565)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−47, 174, 18267)-Net in Base 3 — Upper bound on s

There is no (127, 174, 18268)-net in base 3, because

1 times m-reduction [i] would yield (127, 173, 18268)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34864 018427 436640 442849 450979 814341 984204 593800 463420 621823 599463 537062 968776 320913 > 3¹⁷³ [i]